comment {
Date: 17-10-98

Luke Plant's public fractal formulae, 1998

Some of the below are Fractint types,
others are slightly more original
(although other people have also
done them separately)

}

Julibrot{;

init:
  IF (@plane == 0)
    z = real(pixel)+ flip(imag(p1))
    c = real(p1)+flip(imag(pixel))

    ELSEIF (@plane == 1)
    z = flip(real(pixel)) + imag(p1)
    c = real(p1)+flip(imag(pixel))

  ELSEIF (@plane == 2)
    z = real(pixel) + flip(imag(p1))
    c = flip(real(p1))+imag(pixel)

  ELSEIF (@plane == 3)

   z = flip(real(pixel)) + imag(p1)
   c = flip(real(p1))+imag(pixel)

  ENDIF

loop:
z=sqr(z) + c

bailout:
|z| < @bailout


default:
  title = "Julibrot"
  
  param p1
    caption = "Julibrot parameters"
    default = (0.0,0.0)
  endparam
  
  param plane
    caption = "Julibrot plane"
    default = 0
    enum = "1:Re(c), Im(z0)" "2:Re(c), Re(z0)" \
    "3:Im(c), Im(z0)" "4:Im(c), Re(z0)"
    hint = "shows which parameters are kep constant, \
    ie what the values of parameter P1 are."
  endparam
  
  param bailout
    caption = "Bailout"
    default = 16.0
  endparam
  
switch:
  type = "julibrot"
  bailout = bailout
  plane = plane
  P1=pixel
}


Test2 { ;
; little formula you may find helpful to test the 'Shape'
; colouring method on.  It isn't a fractal in any way - 

z=#pixel, count=0:
count = count + 1
count < 2

default:
  title = "Shape-Test"
    
}

mandel-allout {
; Mandelbrot, but all points bailout
; Use when you want the same colouring method
; for inside as outside
; Use Periodicity checking = off
init:
  z = 0
  complex c = #pixel
  int i = 0
  
loop:
  z = sqr(z) + c
  i=i+1

bailout:
  ; carry on when
  ;  when numiter = #maxiter-1
  ;  IF !(bailout at maxiter only)
  ;    when |z|>bailout
  ; 
  ( (|z| < @bailout) ||  (@maxitonly)) &&  (i < #maxiter)
  
default:
  title = "Mandelbrot all out"
  periodicity = 0
  param bailout
    caption = "Bailout value"
    default = 16.0
  endparam

  param maxitonly
    caption = "Bailout at max. it."
    default = false
    hint = "If enabled, points only bail out after \
    maximum number of iterations"
  endparam
  
switch:
  type = "Julia-allout"
  bailout = bailout
  seed = pixel
  percheck = percheck
  maxitonly = maxitonly
}

Julia-allout {
; Julia, but all points bailout
; Use when you want the same colouring method
; for inside as outside
; Use Periodicity checking = off
init:
  z = #pixel
  complex c = @seed
  int i = 1
  
loop:
  z = sqr(z) + c
  i=i+1

bailout:
  ( (|z| < @bailout) ||  (@maxitonly)) &&  (i < #maxiter)



default:
  periodicity = 0
  title = "Julia all out"
  param bailout
    caption = "Bailout value"
    default = 16.0
  endparam
  
  param seed
    caption = "Julia seed"
    default = (-0.1625,0.687)
  endparam

  param maxitonly
    caption = "Bailout at max. it."
    default = false
    hint = "If enabled, points only bail out after \
    maximum number of iterations"
  endparam

    
switch:
  type = "Mandel-allout"
  bailout = bailout
  maxitonly = maxitonly
}


Test3 {
z=#pixel, count=0:
count = count + 1
count < 2

default:
  title = "Transformation-Test"
    
}


Grid { ; dummy formula - bails out after 1 iteration
int count=0:
count = count + 1
count < 2
default:
  title = "Grid"
  method=onepass
}


Newton-MSet-Mix1 {
; This formula alternates between Newton and Mandelbrot Set
; iterations.

init:
  z = 0
  complex c = #pixel
  bool mand = true      ; do mandelbrot iteration first

loop:
  if (mand)
    z = sqr(z) + c
    mand = false
  else
    z = ((p1 - 1) * z^p1 + @r) / (p1 * z ^ (p1 - 1))
    mand = true
  endif

bailout:
  |z| < @bailout

default:
  title = "Mandelbrot-Newton mix"
  periodicity = 0
  param bailout
    caption = "Mandel Bailout value"
    default = 128.0
  endparam

  param p1
    caption = "Degree"
    default = (3,0)
  endparam

  param r
    caption = "Root"
    default = (1,0)
  endparam

}